This 30 tudor found me last fall. It has a 1963 Illinois license plate still attached, and hadn't been run since. Runs now.
Came with the usual 16" 1935 wheels. Over the years, I've bought other barn find cars that also had 16" wheels. As others have aid, many, many Model A's were converted to 16" wheels back in the day when they were still considered serious transportation by the general public. Easier to get tires, etc.
I am NOT going restore this one and leave it exactly as is as a period piece of history, with crappy paint, dents in fenders and all.
I understand the sentiment of the original poster about his family car. It had 16" wheels in 1960 and will stay that way as a tribute to his own family.